On semigroup ideals and n-derivations in near-rings

A non-empty subset U of a near-ring N is said to be a semigroup left (resp. right) ideal of N if NU ⊆ U (resp. UN ⊆ U) and if U is both a semigroup left ideal and a semigroup right ideal, it will be called a semigroup ideal. In the present paper, we investigate the commutativity of addition and multiplication of near-rings satisfying certain identities involving n-derivations on semigroup ideals and ideals. Furthermore, we study the conditions with semigroup ideals for n-derivations D1 and D2 of N which imply that D1 = D2.